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Multivariate t-distribution

Index Multivariate t-distribution

In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. [1]

29 relations: Chi distribution, Chi-squared distribution, Copula (probability theory), Cumulative distribution function, Degrees of freedom (statistics), Elliptical distribution, Hotelling's T-squared distribution, Independence (probability theory), Joint probability distribution, Location parameter, Mahalanobis distance, Marginal distribution, Mathematical finance, Matrix (mathematics), Matrix t-distribution, Monte Carlo integration, Multivariate normal distribution, Multivariate random variable, Norm (mathematics), Pearson correlation coefficient, Positive-definite matrix, Probability density function, Random matrix, Random variable, Real number, Shape parameter, Statistics, Student's t-distribution, Student's t-test.

Chi distribution

No description.

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Chi-squared distribution

No description.

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Copula (probability theory)

In probability theory and statistics, a copula is a multivariate probability distribution for which the marginal probability distribution of each variable is uniform.

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Cumulative distribution function

In probability theory and statistics, the cumulative distribution function (CDF, also cumulative density function) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.

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Degrees of freedom (statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

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Elliptical distribution

In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution.

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Hotelling's T-squared distribution

In statistics Hotelling's T-squared distribution (T2) is a multivariate distribution proportional to the ''F''-distribution and arises importantly as the distribution of a set of statistics which are natural generalizations of the statistics underlying Student's ''t''-distribution.

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Independence (probability theory)

In probability theory, two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.

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Joint probability distribution

Given random variables X, Y,..., that are defined on a probability space, the joint probability distribution for X, Y,...

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Location parameter

In statistics, a location family is a class of probability distributions that is parametrized by a scalar- or vector-valued parameter x_0, which determines the "location" or shift of the distribution.

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Mahalanobis distance

The Mahalanobis distance is a measure of the distance between a point P and a distribution D, introduced by P. C. Mahalanobis in 1936.

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Marginal distribution

In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset.

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Mathematical finance

Mathematical finance, also known as quantitative finance, is a field of applied mathematics, concerned with mathematical modeling of financial markets.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Matrix t-distribution

In statistics, the matrix t-distribution (or matrix variate t-distribution) is the generalization of the multivariate ''t''-distribution from vectors to matrices.

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Monte Carlo integration

In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers.

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Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions.

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Multivariate random variable

In probability, and statistics, a multivariate random variable or random vector is a list of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value.

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Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

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Pearson correlation coefficient

In statistics, the Pearson correlation coefficient (PCC, pronounced), also referred to as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC) or the bivariate correlation, is a measure of the linear correlation between two variables X and Y. It has a value between +1 and −1, where 1 is total positive linear correlation, 0 is no linear correlation, and −1 is total negative linear correlation.

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Positive-definite matrix

In linear algebra, a symmetric real matrix M is said to be positive definite if the scalar z^Mz is strictly positive for every non-zero column vector z of n real numbers.

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Probability density function

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.

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Random matrix

In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables.

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Random variable

In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Shape parameter

In probability theory and statistics, a shape parameter is a kind of numerical parameter of a parametric family of probability distributions.

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Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Student's t-distribution

In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.

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Student's t-test

The t-test is any statistical hypothesis test in which the test statistic follows a Student's ''t''-distribution under the null hypothesis.

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Redirects here:

Bivariate Student distribution, Bivariate t-distribution, Multivariate Student Distribution, Multivariate Student distribution.

References

[1] https://en.wikipedia.org/wiki/Multivariate_t-distribution

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